Congruence ideal associated to Yoshida lifts

Abstract: This talk will be a report of work in progress with Ming-Lun Hsieh. In analogy with the study of the congruences involving Hecke eigenvalues associated to Eisenstein series, we study congruences involving p-adic families of Hecke eigensystems associated to the space of Yoshida lifts of two Hida families. Our goal is to show that under suitable assumptions, the characteristic ideal of the dual Selmer group associated to the Rankin--Selberg product of the Hida families is contained in the corresponding congruence ideal. We also discuss connections between pseudo-cyclicity of the dual Selmer group and higher codimension Iwasawa theory.

algebraic geometrynumber theory

Audience: researchers in the topic

( slides )

UCSB Seminar on Geometry and Arithmetic